Your emails are stored for as long as you keep them. Emails are only deleted if you delete them. If you delete an email, it will go to Trash, where it will stay for 30 more days. After that, it is deleted forever automatically. Also, if you delete something from Trash manually, that is also deleted forever.

Deleting draft messages is tricky, you must be careful with that: if you click on "Discard", the draft is discarded permanently and you cannot recover it. So if you are composing a lengthy or important email, I recommend using Google Docs, and when the email is written, copy it to Gmail and send it.

Deleting your account:

If your account gets deleted (by you or the university), your data will not be accessible any more, and all the information stored in your account will be deleted eventually. Eventually means that as new user data arrives to the Gmail servers, info from your disabled account will be overwritten.

what Google does with the data it aggregates from them:

Google will use automatic algorhythms to perform spam scanning. As a "side effect" of this, they will use the scan results to display relevant ads for you (or at least what the software considers relevant). So for example if you are reading an email with the words "travelling" and "skiing" in it, you may get ads about these topics on the right hand side.

You can read the details about this in the Terms of Service and the Privacy Policy -- you can find links to both at the bottom of all Google product pages.

Migrating data from your edu account:

When the time comes to leave your university, you can migrate your emails to a different email account using POP access.